Problem ${?}^2$ Network $($the Crashing based problem$)$ Problem $2(4$ POINTS$)$

A construction project has a deadline of $25$ weeks. And there is a penalty of $$50,000$ for every week the project is

delayed after $25$ weeks. The activities in the project, their sequence relationships, and their expected normal times

are shown in the network. The activities, their expected normal times, and their crash costs are shown in the table

below.

Note: There are $4$ paths in this network $($Networks sent to you as a pdf file$).$

Crash Costs $($ $$000)$

$($a$)$ Determine the minimum cost crashing plan to minimize the penalty. List $($in the correct order $0$ all the

activities that will be selected in this plan. Obviously, you will continue to crash only as long as the weekly

crash costs are less than the weekly penalty. $(3\mathrm{.}5$ points$)$

$($b$)$ Determine the total savings from penalty for the above case. $(\frac{1}{2}$ point$)$

Hint for $($b$)$: For example, if you spend $$10,000$ to crash a project by one week, and if your penalty is $$50,000$ for

one week, then your savings from penalty are $$40,000$ for that week.

Hint: There are FOUR paths in this network $($I am giving this information so that you minimize your errors$).$